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Guaranteed control of switched control systems using model order reduction and state-space bisection. (English) Zbl 1432.93043

André, Étienne (ed.) et al., 2nd international workshop on synthesis of complex parameters, SynCoP’15, April 11, 2015, London, UK. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. OASIcs – OpenAccess Ser. Inform. 44, 33-47 (2015).
Summary: This paper considers discrete-time linear systems controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a “state-space bisection” method for synthesizing a control at the reduced-order level, and finally computing an upper bound to the deviations between the controlled output trajectories of the reduced-order model and those of the original model. The effectiveness of our approach is illustrated on several examples of the literature.
For the entire collection see [Zbl 1392.68009].

MSC:

93B11 System structure simplification
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B03 Attainable sets, reachability
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Software:

MPT; PESSOA; CoSyma
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References:

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